Cloud storage has been widely used to team work or cooperation development. Data owners set up groups, generating and uploading their data to cloud storage, while other users in the groups download and make use of it, which is called group data sharing. As all kinds of cloud service, data group sharing also suffers from hardware/software failures and human errors. Provable Data Possession (PDP) schemes are proposed to check the integrity of data stored in cloud without downloading. However, there are still some unmet needs lying in auditing group shared data. Researchers propose four issues necessary for a secure group shared data auditing: public verification, identity privacy, collusion attack resistance and traceability. However, none of the published work has succeeded in achieving all of these properties so far. In this paper, we propose a novel blockchain-based ring signature PDP scheme for group shared data, with an instance deployed on a cloud server. We design a linkable ring signature method called Linkable Homomorphic Authenticable Ring Signature (LHARS) to implement public anonymous auditing for group data. We also build smart contracts to resist collusion attack in group auditing. The security analysis and performance evaluation prove that our scheme is both secure and efficient.